Multisphere Method for Flexible Conducting Space Objects: Modeling and Experiments

Abstract

In the last two decades, concepts have been developed to harness electrostatic forces and torques to enable novel missions, including coulomb formation flying, inflating membrane structures, and detumbling and reorbiting debris touchlessly. The need for faster-than-real-time modeling of the electrostatic forces and torques in these missions has led to the development of the multisphere method (MSM) in which the electrostatic field generated by a charged body is approximated through the use of a series of optimally placed and sized conducting spheres. Although the prior work assumed the charged body was rigid, this paper extends the use of the MSM to flexible shapes. An example of the effectiveness of the MSM approach is explored by matching analytical models of the electric field and capacitance about a line of charge, and then deforming it into a ring while still matching analytic models. However, the core underlying assumption of the shape surface being a conductor remains. The limits of this model are tested via experimental comparison of a thin strip of aluminized Mylar in a constant electric field with the flexible MSM model. Although the new flexible MSM is good at modeling time-varying shapes of pure conductors, the charged thin Mylar sheet dynamics are strongly influenced by dielectric polarization and charge self-emission due to the sharp edges.